Two circles with radius 1 are externally tangent at B and have AB and BC as diameters. A tangent to the circle with diameter BC passes through A, and a tangent to the circle with diameter AB passes through C so that the tangent lines are parallel. Find the distance between the two tangent lines.

Thank you!

Noori Oct 4, 2020

#1**0 **

We can use coordinates. The equations of the lines are y = 1/3*(x + 2) and y = 1/3*(x - 2), and the distance between these lines is 2*sqrt(10)/5.

Guest Oct 4, 2020

#2**-1 **

Sorry, I should have made it clear in the question. I would like some specific steps so that I know how to do these problems in the future. Thank you!

Noori
Oct 4, 2020

#3**+2 **

Hello Noori,

To solve this problem we need to draw a diagram. We know that the tangents will be perpendicular to the radii drawn from their points of tangency, I just proved that yesterday, so we can draw a diagram, assume A' and C' are the centers of the tangent circles. Also, A, B, and C are colinear. Try to find the smallest distance between these lines, and build on this diagram!

Pangolin14
Oct 4, 2020